In this paper, we consider mild solutions to fractional differential inclusions with nonlocal initial conditions. The main results are proved under conditions that (i) the multivalued term takes convex values with compactness of resolvent family of operators; (ii) the multivalued term takes nonconvex values with compactness of resolvent family of operators and (iii) the multivalued term takes nonconvex values without compactness of resolvent family of operators, respectively.

中文翻译：

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通过分解算子族求解具有非局部初始条件的分数阶微分包含物的可解性

在本文中，我们考虑了具有非局部初始条件的分数阶微分包含物的温和解。在以下条件下证明了主要结果：（i）多值项采用凸值且算子的分解算子族较为紧凑；（ii）多值项采用非凸值且算子的分解族不紧缩（iii）多值项采用非凸值而算子的分解族不紧缩。